UCONN should never have "objected". You deal with the rules as they are. If UCONN didn't want to end up in Palo Alto or wherever in the 3rd and 4th rounds, they should have put their bid in. Honestly I don't see where it matters one way or the other. If you have 1 seeds of UCONN, Duke, ND and say Stanford, it's pretty easy to see where they'd all be sent... and what bracket they'd be in.
It makes no sense to me that any UCONN fans would be outraged, or even upset at this. UCONN didn't put a bid in. So the committee chose the best sites they could based on who made bids.
You are making two separate points.
I think there are time that when objects to a decision, one should then refuse to take advantage of the policy, while there are other situations where your objection to a decision should be followed up with a refusal to accept the benefits of the decision. The second decision does not also have to follow form the position about the first.
In this specific case, I happen to think the NCAA decision to abandon predetermined sites and let the top seeds host the first two rounds was sound (as an aside, I think I have a better approach, but the committee doesn't yet agree with me). However, I disagree with the NCAA that the Regionals should be hosted by teams in the tournament.
I don't see this as a principled vote. I understand and respect those who chose to vote in favor of this change. But I'm on the side of those opposed, and therefore I commend UConn for standing in opposition to the policy.
Once the policy is enacted, one can choose to accept the decision, and make the best option for your individual school, which might mean UConn should bid, or you can decide that your view on opposition is sufficiently strong that you choose not to bid for a regional, even at a potential cost to your own school.
This is a tougher call, but I respect UConn for having the courage of its convictions to refuse to enter a bid. But again, this isn't really a case of principles, it is a case of different views on how best to improve the sport. If some school objected to the decision, and followed it up with a bid, I wouldn't accuse them of hypocrisy. It might well be the appropriate action.